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Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems

URN to cite this document: urn:nbn:de:bvb:703-epub-2003-0

Title data

Grüne, Lars ; Kellett, Christopher M.:
Strong implication-form ISS-Lyapunov functions for discontinuous discrete-time systems.
Department of Mathematics, University of Bayreuth
Bayreuth , 2014

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Gruene_Kellett_strong_impl-form_iss-lyap_fct_discont_discr-time_sys_2014.pdf - Accepted Version
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Project information

Project title:
Project's official titleProject's id
Marie-Curie Initial Training Network "Sensitivity Analysis for Deterministic Controller Design" (SADCO)"264735-SADCO
ARC Future FellowshipFT1101000746
Humboldt Research Fellowshipohne Angabe

Project financing: 7. Forschungsrahmenprogramm für Forschung, technologische Entwicklung und Demonstration der Europäischen Union
Alexander-von-Humboldt Foundation
Australien Research Council (ARC)

Abstract

Input-to-State Stability (ISS) and the ISS-Lyapunov function have proved to be useful tools for the analysis and design of nonlinear systems in a variety of contexts. Motivated by the fact that many feedback control laws, such as model predictive control or event-based control, lead to discontinuous discrete-time dynamics, we investigate ISS-Lyapunov functions for such systems. ISS-Lyapunov functions were originally introduced in a so-called implication-form and, in many cases, this has been shown to be equivalent to an ISS-Lyapunov function of dissipation-form. However, for discontinuous dynamics, we demonstrate via an example that this equivalence no longer holds. We therefore propose a stronger implication-form ISS-Lyapunov which re-establishes the equivalence to dissipation-form ISS-Lyapunov functions and to the ISS property for discontinuous systems.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): An extended version of this paper was submitted to the IEEE Transactions
on Automatic Control.
Keywords: input-to-state stability (ISS); Lyapunov functions; discrete-time systems
DDC Subjects: 500 Science > 510 Mathematics
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne)
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-2003-0
Date Deposited: 17 Apr 2015 07:24
Last Modified: 28 Mar 2019 15:26
URI: https://epub.uni-bayreuth.de/id/eprint/2003

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